An overlay is a layer of strengthening product — builder gel, acrylic or dip powder — applied over the natural nail at its natural length. No tips, no forms, no added length: the point is armour, not architecture. Overlays are the answer for people whose nails grow fine but break at the first collision, and for anyone who wants the durability of an enhanced set while keeping their own proportions.
The overlay-versus-extension question is really a question about your natural length: happy with it, overlay; want more, extension. Everything else — colours, french tips, finishes, art — sits identically on either foundation, which is why a design can be decided first and the engineering discussed with your tech after. BIAB worn on natural nails is the overlay most people are getting today, whether or not the word is used.